Best Known (12, 12+14, s)-Nets in Base 25
(12, 12+14, 126)-Net over F25 — Constructive and digital
Digital (12, 26, 126)-net over F25, using
- t-expansion [i] based on digital (10, 26, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(12, 12+14, 175)-Net over F25 — Digital
Digital (12, 26, 175)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2526, 175, F25, 14) (dual of [175, 149, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2526, 312, F25, 14) (dual of [312, 286, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2526, 312, F25, 14) (dual of [312, 286, 15]-code), using
(12, 12+14, 21927)-Net in Base 25 — Upper bound on s
There is no (12, 26, 21928)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 2 220739 471425 796519 289522 060328 800065 > 2526 [i]